Having run 5/3/1 for the best part of a year I think all of the shortcomings relate to weaker lifters. I think if you have at least 3/2/4 plates for squat/bench/dead it works well. In fact I think the stronger you are, the better it works.
1. If used by weaker lifters, they end up not lifting enough weight. Often they're not lifting to their full capabilities through technique issues rather than strength and low volume doesn't fix that although Boring but Big can.
2. Again for weaker lifters, 4 weekly deloads are not needed. They aren't lifting enough to warrant that.
3. For powerlifters there's not enough low rep' stuff.
There's probably more but those are the main ones. My main bugbear with it is the deload issue.
Don't call it a comeback